实验报告-时间序列

实验报告-平稳时间序列模型的建立08经济统计I60814030王思瑶一 实验目的从观察到的化工生产过程产量的70个数据样本出发，通过对模型的识别、模型的定价、模型的参数估计等步骤建立起适合序列的模型。以下是化工生产过程的产量数据：obsBFobsBF1473658264374532338544713936538405466441487554255841434595944571048455011714662123547441357486414404943155850521644513817805259185553551937544120745553215156492257573423505835246059542545604526576168275062382845635029256460305965393150665932716740335668573474695435507023可以明显看出序列均值显著非零，所以用样本均值作为其估计对序列进行零均值化。obsBF零均值化后的数据YobsBF零均值化后的数据Y147-4.1285736586.8714326412.871433745-6.12857323-28.1285738542.8714347119.871433936-15.12857538-13.1285740542.8714366412.871434148-3.128577553.8714342553.87143841-10.128574345-6.128579597.8714344575.871431048-3.128574550-1.12857117119.87143466210.871431235-16.128574744-7.1285713575.87143486412.871431440-11.128574943-8.1285715586.8714350520.871431644-7.128575138-13.12857178028.8714352597.8714318553.8714353553.871431937-14.128575441-10.12857207422.8714355531.871432151-0.128575649-2.1285722575.871435734-17.128572350-1.128575835-16.1285724608.8714359542.871432545-6.128576045-6.1285726575.87143616816.871432750-1.128576238-13.128572845-6.128576350-1.128572925-26.1285764608.8714330597.871436539-12.128573150-1.1285766597.87143327119.871436740-11.1285733564.8714368575.87143347422.8714369542.871433550-1.128577023-28.12857二实验步骤1.模型识别零均值平稳序列的自相关函数与偏相关函数的统计特性如下：模型 AR(n) MA(m) ARMA(n,m)自相关函数 拖尾 截尾 拖尾偏自相关函数 截尾 拖尾 拖尾所以，作零均值化后数据的自相关函数与偏自相关函数图Date: 04/25/11 Time: 22:35Sample: 2001 2070Included observations: 70AutocorrelationPartial CorrelationACPACQ-StatProb*| . |*| . |1-0.382-0.38210.6380.001. |* |. |* |20.3250.20918.4440.000*| . |. | . |3-0.193-0.01821.2340.000. |*. |. | . |40.090-0.04921.8570.000.*| . |.*| . |5-0.162-0.12623.9000.000. | . |.*| . |60.014-0.09423.9160.001. | . |. | . |70.0120.06523.9280.001.*| . |.*| . |8-0.085-0.07924.5190.002. | . |. | . |90.039-0.05124.6440.003. | . |. |*. |100.0330.08024.7360.006. |*. |. |*. |110.0900.12525.4260.008.*| . |. | . |12-0.077-0.05425.9420.011. | . |. | . |130.063-0.04526.2910.016. | . |. |*. |140.0510.13426.5240.022. | . |. |*. |15-0.0060.07926.5280.033. |*. |. |*. |160.1260.14528.0160.031.*| . |. | . |17-0.090-0.04028.7920.036. | . |.*| . |180.017-0.08428.8200.051.*| . |. | . |19-0.099-0.01729.7950.054. | . |. | . |200.006-0.03629.7980.073. | . |. | . |210.0150.05529.8200.096. | . |. | . |22-0.037-0.01529.9680.119. | . |. | . |230.013-0.05129.9850.150. | . |. | . |240.0100.01029.9970.185. | . |. | . |250.015-0.01630.0230.223. | . |. | . |260.0360.02330.1720.261. | . |. | . |27-0.016-0.03630.2020.305. | . |. | . |280.0330.03030.3350.347. | . |. | . |29-0.057-0.01530.7350.378. | . |. | . |300.051-0.00331.0640.412.*| . |. | . |31-0.070-0.05331.7060.431. | . |. | . |320.057-0.00332.1410.460由上图可知Autocorrelation与Partial Correlation序列均有收敛到零的趋势，可以认为Y的自相关函数与偏自相关函数均是拖尾的，所以初步判断该序列适合ARMA模型。2.模型定阶（1）根据Pandit-Wu建模方法，拟建ARMA（2，1）模型，在EViews命令栏中输入：LS Y AR(1) AR(2) MA(1)，得到如下结果：Dependent Variable: YMethod: Least SquaresDate: 04/27/11 Time: 16:11Sample (adjusted): 2003 2070Included observations: 68 after adjustmentsConvergence achieved after 16 iterationsBackcast: 2002VariableCoefficientStd. Errort-StatisticProb.AR(1)-0.8371280.327087-2.5593430.0128AR(2)-0.0794100.190590-0.4166520.6783MA(1)0.5313600.3171141.6756090.0986R-squared0.223430Mean dependent var-0.128570Adjusted R-squared0.199535S.D. dependent var11.97136S.E. of regression10.71062Akaike info criterion7.623463Sum squared resid7456.629Schwarz criterion7.721383Log likelihood-256.1978Durbin-Watson stat1.824445Inverted AR Roots-.11-.73Inverted MA Roots-.53令a2=resid ，在Eviews命令行中输入：genr a2=resid再输入：scat a2 a2(-1)看该模型的残差与其滞后一期之间的散点图：从上图看不出有相关趋势，而且D.W值为1.824445，说明不存在相关性，因此可以初步认为ARMA（2，1）模型是适应的。（2）根据Pandit-Wu建模方法，再建ARMA（4，3）模型，在EViews命令栏中输入：LS Y AR(1) AR(2) AR(3) AR(4) MA(1) MA(2) MA(3)，得到如下结果：Dependent Variable: YMethod: Least SquaresDate: 04/27/11 Time: 16:36Sample (adjusted): 2005 2070Included observations: 66 after adjustmentsConvergence achieved after 191 iterationsBackcast: 2002 2004VariableCoefficientStd. Errort-StatisticProb.AR(1)-0.5988740.145198-4.1245440.0001AR(2)0.3121000.1230012.5373790.0138AR(3)0.8709760.1186357.3416630.0000AR(4)0.1743630.1293781.3477020.1829MA(1)0.3288360.0492186.6812140.0000MA(2)-0.2887470.056156-5.1418340.0000MA(3)-0.9400540.053871-17.450060.0000R-squared0.236761Mean dependent var-0.007358Adjusted R-squared0.159143S.D. dependent var11.37949S.E. of regression10.43479Akaike info criterion7.628172Sum squared resid6424.210Schwarz criterion7.860409Log likelihood-244.7297Durbin-Watson stat1.907327Inverted AR Roots.94-.22-.66-.64i-.66+.64iInverted MA Roots.97-.65+.74i-.65-.74i由上面结果可以看出：ARMA（4，3）模型的残差平方和Sum squared resid为6424.210， ARMA（2，1）模型的残差平方和Sum squared resid为7456.629，因此ARMA（4，3）拟合效果更好；而且ARMA（4，3）模型的D.W值为1.907327，大于ARMA（2，1）模型的D.W值1.824445，说明ARMA（4，3）模型的拟合效果更好；RMA（4，3）模型AIC值为7.628172，比ARMA（2，1）模型的7.623463稍大，但并不明显。因此模型ARMA（4，3）比模型ARMA（2,1）更好。（3）根据Pandit-Wu建模方法，再建模型ARMA（6，5），在EViews命令栏中输入：LS Y AR(1) AR(2) AR(3) AR(4) AR(5) AR(6) MA(1) MA(2) MA(3) MA(4) MA(5) ,得到如下结果：Dependent Variable: YMethod: Least SquaresDate: 04/27/11 Time: 16:46Sample (adjusted): 2007 2070Included observations: 64 after adjustmentsConvergence achieved after 124 iterationsBackcast: OFF (Roots of MA process too large)VariableCoefficientStd. Errort-StatisticProb.AR(1)0.1548380.2155130.7184610.4756AR(2)0.0190600.2076730.0917810.9272AR(3)0.1427820.1214871.1752860.2451AR(4)0.2354670.1697331.3872820.1712AR(5)0.6786490.2092393.2434150.0020AR(6)0.1157840.1815760.6376610.5264MA(1)-0.6109750.318997-1.9153020.0609MA(2)0.5842470.3334971.7518800.0856MA(3)-0.1050150.308324-0.3406000.7348MA(4)-0.5608250.369143-1.5192630.1346MA(5)-1.1605710.430714-2.6945260.0094R-squared0.596802Mean dependent var-0.003570Adjusted R-squared0.520727S.D. dependent var11.32423S.E. of regression7.839709Akaike info criterion7.111439Sum squared resid3257.435Schwarz criterion7.482497Log likelihood-216.5661Durbin-Watson stat2.318205Inverted AR Roots1.07.28+.89i.28-.89i-.18-.65+.51i-.65-.51iEstimated AR process is nons